We're dividing 501777 by 7 
The aim is to understand the frequency of 7 in 501777.

Advancing to step 1:
7 goes into 5 0 times with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 7

Advancing to step 2:
If we divide 50 by 7, we get 7 and a remainder of 1.
Write down 7 as next digit of the result. 
Result so far: 7.0
Deduct 49 from 50 and we're left with 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 7

Going ahead to step 3:
When dividing 11 by 7, we get 1 with a remainder of 4.
The number 1 becomes the next digit in our result. 
Result so far: 71.0
Subtracting 7 from 11 leaves us with 4.
Take the next digit (7) from the dividend and append it to 4, then repeat: 47 / 7

Advancing to step 4:
47 divided by 7 is 6 with a remainder of 5.
Put 6 as the next digit of the answer. 
Result so far: 716.0
Subtracting 42 from 47 leaves us with 5.
Take the next digit (7) from the dividend and append it to 5, then repeat: 57 / 7

Moving on to step 5:
7 can be fit into 57 8 times, resulting in a remainder of 1.
The number 8 becomes the next digit in our result. 
Result so far: 7168.0
Subtracting 56 from 57 leaves us with 1.
Append the next digit (7) from the dividend to 1 and continue with: 17 / 7

On to step 6:
17 divided by 7 is 2 with a remainder of 3.
Use 2 as the next digit of our solution. 
Result so far: 71682.0
Deduct 14 from 17 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 7:
The number 7 fits into 30 4 times, leaving a remainder of 2.
The next digit of our result is 4. 
Result so far: 71682.4
If we subtract 28 from 30, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 8:
The number 7 fits into 20 2 times, leaving a remainder of 6.
Put 2 as the next digit of the answer. 
Result so far: 71682.42
If we subtract 14 from 20, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 9:
The number 7 fits into 60 8 times, leaving a remainder of 4.
The next digit of our result is 8. 
Result so far: 71682.428
If we subtract 56 from 60, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 10:
7 goes into 40 5 times with a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 71682.4285
The remainder is 5 after subtracting 35 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 11:
7 goes into 50 7 times with a remainder of 1.
Write down 7 as next digit of the result. 
Result so far: 71682.42857
Subtracting 49 from 50 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 12:
10 divided by 7 is 1 with a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 71682.428571
Subtracting 7 from 10 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 13:
The number 7 fits into 30 4 times, leaving a remainder of 2.
The next digit of our result is 4. 
Result so far: 71682.4285714
If we subtract 28 from 30, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 14:
20 divided by 7 is 2 with a remainder of 6.
Record the quotient 2 as the next digit in the result. 
Result so far: 71682.42857142
Subtract 14 from 20 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

The final outcome is 71682.42857142, with a leftover of 6e-09.